1. Field of the Invention
The present invention relates to communication systems and, more particularly, to channel estimation in communication systems such as orthogonal frequency domain multiplexing or other systems that rely on channel estimation.
2. Description of the Related Art
Orthogonal frequency domain multiplexing (OFDM) is a common modulation strategy for a variety of commercially significant systems, including for digital subscriber line (DSL) communication systems and a number of implementations of the various IEEE 802.xx standards for wireless communication systems. Often, an OFDM receiver will perform one or more functions that require channel estimation to allow the receiver to acquire a signal and to improve signal quality before the receiver begins extracting bits.
OFDM receivers generally need to obtain signal timing information from a received signal to help identify the start of a symbol within the received signal. A symbol is a predetermined number Nb of bits uniquely mapped into a waveform over a predetermined, finite interval or duration. Each possible collection of bits is mapped to a unique signal according to the mapping or modulation strategy dictated by the OFDM scheme. Once an OFDM receiver determines when a symbol begins within the received signal, the receiver performs additional processing to improve the quality of the received signal. In the processing to improve signal quality, the receiver attempts to achieve a target bit error rate (BER), often by implementing a linear filter, or equalizer, to condition the input signal. The received signal can be significantly distorted by channel imperfections. Ideally, the equalizer corrects the distortions introduced by the channel completely so that the receiver can demodulate the signal with performance limited only by the noise level.
OFDM, unlike most other modulation strategies commonly used in communication systems, can include two equalizers to improve signal quality: a time equalizer (TEQ) and a frequency equalizer (FEQ). Some OFDM applications such as DSL include a time equalizer while others, such as systems that implement current wireless standards, do not demand a time equalizer. All practical OFDM receivers have a frequency equalizer. Whether a receiver includes a time equalizer or only a frequency equalizer, the receiver needs to perform channel estimation to at least initially determine values of the equalizer coefficients before the equalizer can be used to improve the signal quality. Determining the coefficients for frequency equalizers is typically performed in the frequency domain.
Conventional OFDM receiver circuitry down converts the received signal to baseband and then analog-to-digital converts that signal to produce the information signal s(n) that is input into the OFDM processing circuitry shown in FIG. 11. The signal s(n) is input 1101 to a first processing element 1110 that removes the cycle prefix (CP) from the signal s(n). A conventional OFDM transmitter adds a CP of length NCP, which consists of the last NCP samples, to a unique signal waveform of length N so that the digital signal that the transmitter converts to analog is of length N+NCP. The initial step of the receiver's reverse conversion process then is to remove and discard the added cycle prefix NCP samples. Following that step, a serial to parallel conversion element 1120 organizes and converts the serial signal into parallel for further processing. The cycle prefix can be removed either before or after the serial to parallel conversion.
The parallel data output from the element 1120 is provided to a fast Fourier transform (FFT) processor 1130 that converts the time domain samples s(n) to a set of frequency domain samples Ri(k) for processing. The received OFDM symbol is assumed to be corrupted by the channel, which is assumed for OFDM to introduce amplitude and phase distortion to the samples from each of the frequencies used in the OFDM system. The FEQ 1150 applies an amplitude and phase correction specific to each of the frequencies used in the OFDM system to the various samples transmitted on the different frequencies. To determine the correction to be applied by the FEQ 1150, the FEQ 1150 needs an estimate of the channel's amplitude and phase variations from ideal at each frequency. In FIG. 11, the frequency domain channel estimate 1140 element determines the channel estimate that is used by the FEQ 1150.
A conventional OFDM channel estimator 1140 used in FIG. 11 typically uses a pilot tone sequence or other signal that has predictable characteristics such as known bits and carrier locations. The pilot tones are generally dictated by the relevant standards. The frequency equalizer 1150 receives the signals from the fast Fourier transform processor 1130 and the channel estimates from the estimator 1140 and equalizes the signal. The output of the equalizer 1150 is provided to a parallel to serial element 1160 that converts the parallel outputs of the equalizer to a serial signal that is then provided to the demodulator 1170. The structure and function of the demodulator varies and generally corresponds to a standard or particular OFDM communication scheme.
In many applications, there is a requirement to model an unknown system or process with a transfer function. The transfer function takes the form of either an infinite impulse response (IIR) or a finite impulse response (FIR) polynomial or filter. The former is also referred to as an auto-regressive moving average (ARMA) model and the latter simply as a moving average (MA) model.
The process of system identification or, equivalently, characterization, can typically be described as shown in FIG. 1. The input 101 to the unknown system 110 and the output 112 are used by the identification process to determine the ARMA or MA models. Modern identification methods are digitally implemented, so the signals s 101 and y 112 are assumed to be sampled, without a loss of generality on the methods' applicability and performance. From linear system theory, the relationship between the input and output signals is simply defined as a convolution, that is,
                              y          ⁡                      [            n            ]                          =                              ∑                          l              =                              -                ∞                                                    +              ∞                                ⁢                                    h              ⁡                              [                l                ]                                      ⁢                                          s                ⁡                                  [                                      n                    -                    l                                    ]                                            .                                                          (        1        )            Therefore, if the samples of the input signal s 101 are known and the unknown system's output signal y 112 samples are measured, the linear estimation of the unknown system can be achieved though various strategies.
The signals s 101 and y 102 are better described in a sampled system by adding the sampling index n that maps the value of each signal sample to an interval of time. The modeled unknown system response h[l] has the same sampling interval as the signals s[n] and y[n]. The discussions here assume that input and output signals are sampled at the same sampling interval. Variations on these assumptions do not affect performance of presently preferred implementations of the present invention.
The simplest strategy to identify an unknown system is to use an input signal for system identification that is s[0]=1, s[n]=0 for values of n≠0, and ranging between −∞ and +∞. This impulse response is termed a Dirac delta function and it has the desired effect in equation (1) of y[n]=h[n]. However, in most practical systems, using a Dirac delta function for system identification is not possible due to the practical difficulty in generating such an input signal, combined with hindering operational conditions such as the typical throughput rates in communication systems.
Since the right side of equation (1) is a dot-product definition, the output 112 is observed over N samples and the MA time span of h[l] is assumed to not be significant beyond L samples, then a matrix formulation of equation (1) is readily obtained:y=Hs=Sh  (2)where the N-by-L matrix H(S) has rows with the time-shifted samples, as a function of n, and the vector L-by-1 s(h) is fixed over the time span in y. That is, the entries in the vector y arey[m]=[y[n]y[n+1] . . . y[n+N+1]]T  (3).The time index m is used to denote the possibility that the time-series of the vector y may not have a one-to-one correspondence with the input samples y. On the other hand, the index m in an OFDM system does have a one-to-one correspondence with the received OFDM symbol, defined as the time interval containing N=FFT length+cycle prefix samples. For example, in the WiMAX standard, this value can be N=1024+128=1152 samples.
Linear algebra notation is used to describe the operations due to its succinct representation and due to its immediate parallel to a hardware multiply-and-accumulate operation that performs a dot-product between two vectors, or the multiplication of a matrix row and a vector, as in equation (2). Those skilled in the art generally also exploit symmetric properties in the matrix to reduce complexity in this matrix-vector multiplication.